Geometry, electronic structure, and magnetism of small Nin (n = 2–6, 8, 13) clusters

Co-Promoted CoNi Bimetallic Nanocatalyst for the Highly Efficient Catalytic Hydrogenation of Olefins

Bimetallic catalysts, especially non-noble metals, hold great potential for substituting for noble metals in catalytic hydrogenation. In present study, a series of Co_xNi_y (x + y = 6) bimetallic catalysts were prepared through the impregnation-reduction method and cyclohexene was chosen as probe-molecule to study the promotion effect of Co on the catalytic olefin hydrogenation reactions. Meanwhile, density functional theory (DFT) was utilized to investigate the formation energies and the charge distribution of CoNi bimetals, as well as the transition state (TS) searches for hydrogen dissociation and migration. The results suggest that bimetals tend to have superior catalytic performance than pure metals, and Co₃Ni₃ shows the highest catalytic activity on the cyclohexene hydrogenation. It was found that the charge transfer from Co to Ni and the alloying give rise to the refinement of CoNi grains and the improvement of its catalytic activity and stability. Thus, it may be possible to obtain better catalytic performance by tuning the metal/metal atomic ratio of bimetals.

Structure and size-dependent vibrational and thermal properties of Ni clusters: A systematic ab initio approach

There is scarce information on the vibrational and thermal properties of small Ni clusters. Here, the outcomes of ab initio spin-polarized density functional theory calculations on the size and geometry effects upon the vibrational and thermal properties of Ni_n (n = 13 and 55) clusters, are discussed. For theses clusters a comparison is presented between the closed shell symmetric octahedral (O_h) and the icosahedral (I_h) geometries. The results indicate that the I_h isomers are lower in energy. Besides, ab initio molecular dynamics runs at T = 300K show that Ni₁₃ and Ni₅₅ clusters transform from their initial O_h geometries towards the corresponding I_h ones. For Ni₁₃, we also consider the lowest energy less symmetric layered 1-3-6-3 structure, and the cuboid, recently observed experimentally for Pt₁₃, which is competitive in energy but is unstable, as phonon analysis reveals. We calculate their vibrational density of states (νDOS) and heat capacity, and compare with the Ni FCC bulk counterpart. The characteristic features of the νDOS curves of these clusters are interpreted in terms of the clusters' sizes, the interatomic distance contractions, the bond order values as well as the internal pressure and strains of the clusters. We find that the softest possible frequency of the clusters is size and structure-dependent, being the smallest for the O_h ones. We identify mostly shear, tangential type displacements involving mainly surface atoms for the lowest frequency of the spectra of both I_h and O_h isomers. For the maximum frequencies of these clusters the central atom shows anti-phase movements against groups of nearest neighbor atoms. An excess of heat capacity at low temperatures with respect to the bulk is found, while at high temperatures a constant limiting value, close but lower to the Dulong and Petit value, is determined.

Different Phenomena in Magnetic/Electrical Properties of Co(II) and Ni(II) Isomorphous MOFs

Two unprecedented and stable metal-organic frameworks, {[Co₂(H₂O)₂(L)(OH)]·2.5H₂O·0.5DMF} _n (1) and {[Ni₂(H₂O)₂(L)(OH)]·1.75H₂O} _n (2), have been synthesized (H₃L = 5-(5-carboxy-pyridin-3-yloxy)-isophthalic acid, DMF = N,N-dimethylformamide). Structural analysis shows that 1 and 2 are heteronuclear isomorphous, possessing a three-dimensional (3D) (4,8)-connected flu/fluorite topological framework formed through the interconnection of tetranuclear butterfly {M₄(COO)₆(OH)₂} clusters and the ligands. Although the frameworks of these two compounds are similar, their magnetic properties are different. Compound 1 exhibits an antiferromagnetic interaction in the high-temperature region, while 2 shows a weak ferromagnetic interaction in the whole-temperature region. Furthermore, considering the presence of hydroxyl groups and water molecules in the frameworks, we tested their proton conductivity. The efficient proton transfer pathway in the framework endowed 1 and 2 with excellent proton conductivities of 9.07 × 10^-5 and 1.29 × 10^-4 S·cm^-1 at 363 K and 98% relative humidity (RH), respectively.

DFT insights into structural effects of Ni-Cu/CeO2 catalysts for CO selective reaction towards water-gas shift

The water-gas shift (WGS) reaction is a key step in hydrogen production, particularly to meet the high-purity H2 requirement of PEM fuel cells. The catalysts currently employed in large-scale WGS plants require a two-step process to overcome thermodynamic and kinetic limitations. Ni-Cu/CeO2 solids are promising catalysts for the one-step process required for small-scale applications, as the addition of Cu hinders undesired methanation reactions occurring on Ni/CeO2. In this work, we performed calculations on Ni4-xCux/CeO2(111) systems to evaluate the influence of cluster conformation on the selectivity towards water-gas shift. The structure and miscibility of CeO2-supported Ni4-xCux clusters were investigated and compared with those of gas-phase clusters to understand the effect of metal-support interactions. The adsorption of CO onto apical Ni and Cu atoms of Ni4-xCux/CeO2(111) systems was studied, and changes in the C-O bond strength were confirmed at the electronic level by investigating shifts in the 3σ and 1π orbitals. The selectivity towards WGS was evaluated using Brønsted-Evans-Polanyi relations for the C-O activation energy. Overall, a strengthening of the C-O bond and an increase in CO dissociation energy were verified on Cu-containing clusters, explaining the improvement in selectivity of Ni4-xCux/CeO2(111) systems.

Tuning the Catalytic Activity of Pd x Ni y (x + y = 6) Bimetallic Clusters for Hydrogen Dissociative Chemisorption and Desorption

Density functional theory was used to study dissociative chemisorption and desorption on Pd _x Ni _y (x + y = 6) bimetallic clusters. The H₂ dissociative chemisorption energies and the H desorption energies at full H saturation were computed. It was found that bimetallic clusters tend to have higher chemisorption energy than pure clusters, and the capacity of Pd₃Ni₃ and Pd₂Ni₄ clusters to adsorb H atoms is substantially higher than that of other clusters. The H desorption energies of Pd₃Ni₃ and Pd₂Ni₄ are also lower than that of the Pd₆ cluster and comparable to that of the Ni₆ cluster, indicating that it is easier to pull the H atom out of these bimetallic catalysts. This suggests that the catalytic efficiency for specific Pd _x Ni _y bimetallic clusters may be superior to bare Ni or Pd clusters and that it may be possible to tune bimetallic nanoparticles to obtain better catalytic performance.

Uniaxial magnetic anisotropy energy of bimetallic Co-Ni clusters from a first-principles perspective

Along with the growing precision in the control of matter at increasingly smaller size scales, a field of research, based onto magnetic materials of technical interest, such as bimetallic clusters, has been developed in very recent years. Thereby, here, we report on a complete study of bimetallic clusters composed of cobalt and nickel with up to 7 atoms using ab initio methods in the GGA approach. We applied an unrestricted search method based on the tensor of inertia eigenvalues to find the most stable configurations of the clusters, obtaining a diverse set of structures with different geometric properties. We explored the effect of composition on the structural properties, the chemical stability, the magnetization and the magnetic anisotropy energy (MAE) of the so-obtained systems. Our results indicate that the behavior of the clusters is mainly governed by the Co-Co interaction and to a lesser extent by the Co-Ni and Ni-Ni interactions. Furthermore, for a given cluster size the magnetic moment increases by 2 μB/Co-substitution plus 1 μB/Ni-substitution coming from the cobalt and nickel core d-states, while in some cases unpaired hybrid s-electrons can also give rise to itinerant magnetism. These features have been analyzed with the help of a Jellium model and have important consequences for the magnetism and the magnetic anisotropy of the clusters. The magnetic behavior and MAE present complex and intriguing landscapes, which suggests the possibility of finely controlling the magnetic states, by tuning the cluster composition, aiming at technical implementation in fields such as molecular magnetism or quantum computation. In particular, cases such as Co6Ni, Co4Ni3, CoNi6 Co2Ni5 and Co3Ni3 present high relative stability and enhanced magnetic moments (around 10 μB), what makes them promising candidates for applications such as subnanometer magnetic information storage.

Superatomic states in nickel clusters: Revising the prospects for transition metal based superatoms

The geometries and electronic structures of small Ni_n^z clusters (n = 8, 9, 10) (z = 0, ±1, 2) have been elucidated for a range of multiplicities for each cluster size and charge, using density functional theory methods. These clusters have been found to conform in part to the existing superatomic model, with each cluster having a filled superatomic S-orbital, filled or partially filled superatomic P-orbitals, and empty or partially filled superatomic D-orbitals. Despite local states of mixed symmetry being present in the immediate vicinity of the Fermi energy, the addition or removal of a single electron from these systems causes a significant shift in the relative energies of the superatomic orbitals. In addition, this study demonstrates the possibility for d-electrons to contribute into superatomic orbitals to a greater or lesser extent, depending on the local environment. In summary, these observations lead to the prospect of a predictive model for electronic shell closings in some transition metal cluster systems.

First principles study of bimetallic Ni13-nAgn nano-clusters (n = 0-13): Structural, mixing, electronic, and magnetic properties

Using spin polarized density functional theory based calculations, combined with ab initio molecular dynamics simulation, we carry out a systematic investigation of the bimetallic Ni_13-nAg_n nano-clusters, for all compositions. This includes prediction of the geometry, mixing behavior, and electronic properties. Our study reveals a tendency towards the formation of a core-shell like structure, following the rule of putting Ni in a high coordination site and Ag in a low coordination site. Our calculations predict negative mixing energies for the entire composition range, indicating mixing to be favored for the bimetallic small sized Ni-Ag clusters, irrespective of the compositions. The magic composition with the highest stability is found for the NiAg₁₂ alloy cluster. We investigate the microscopic origin of a core-shell like structure with negative mixing energy, in which the Ni-Ag inter-facial interaction is found to play a role. We also study the magnetic properties of the Ni-Ag alloy clusters. The Ni dominated magnetism consists of parallel alignment of Ni moments while the tiny moments on Ag align in anti-parallel to Ni moments. The hybridization with the Ag environment causes reduction of Ni moment.

An efficient genetic algorithm for structure prediction at the nanoscale

We have developed and implemented a new global optimization technique based on a Lamarckian genetic algorithm with the focus on structure diversity. The key process in the efficient search on a given complex energy landscape proves to be the removal of duplicates that is achieved using a topological analysis of candidate structures. The careful geometrical prescreening of newly formed structures and the introduction of new mutation move classes improve the rate of success further. The power of the developed technique, implemented in the Knowledge Led Master Code, or KLMC, is demonstrated by its ability to locate and explore a challenging double funnel landscape of a Lennard-Jones 38 atom system (LJ₃₈). We apply the redeveloped KLMC to investigate three chemically different systems: ionic semiconductor (ZnO)_1-32, metallic Ni₁₃ and covalently bonded C₆₀. All four systems have been systematically explored on the energy landscape defined using interatomic potentials. The new developments allowed us to successfully locate the double funnels of LJ₃₈, find new local and global minima for ZnO clusters, extensively explore the Ni₁₃ and C₆₀ (the buckminsterfullerene, or buckyball) potential energy surfaces.

Enhancing 4-propylheptane dissociation with nickel nanocluster based on molecular dynamics simulations

In the present work, a 0.4nm nickel cluster has been theoretically studied. Its equilibrium structural parameters have been calculated by the DFT method based on the PBEH1PBE hybrid functional and split-valence basis set Lanl2DZ including effective core potentials. We have systematically considered diverse spin states of this cluster and find out its ground state. The relative stability of these states depends on the HOMO-LUMO gap. The interaction of the Ni₆ with 4-propylheptane С₁₀Н₂₂ has been studied to simulate the process of catalytic cracking of hydrocarbons. The optimization of this structure has been performed by the ωPBE/Lanl2DZ_ecp method (the TeraChem V.1.9 program package) with no symmetry restrictions; the electron shells of the metal were described by effective core pseudopotentials. For visualization and quantitative estimation of the bonding bonds between the nickel nanocluster and 4-propylheptane, the analysis of weak interactions based on RGD has been performed. To confirm the proposition about the formation of Ni-H bonds, we have scrutinized critical points of electronic density. Values of laplasian of electronic density and Bader atomic charge distribution in the global minimum of the total energy have been estimated by the AIMAll 15.05.18 program suite. Finally, we have simulated interaction of Ni₆ with 4-propylheptane in terms of the Born-Oppenheimer ab initio molecular dynamics. The results of the molecular dynamics simulation provide pair radial distribution function CH at 1500°C and a detailed picture of the processes occurring in the system.

Molecular simulation of CH4/CO2/H2O competitive adsorption on low rank coal vitrinite

The competitive adsorptions of CH₄/CO₂/H₂O on coal vitrinite (DV-8, C₂₁₄H₁₈₀O₂₄N₂) were computed based on density function theory (DFT) and grand canonical Monte Carlo (GCMC).

DFT studies of Ni cluster on graphene surface: effect of CO2 activation

The activation of CO₂ can be significantly enhanced by Ni cluster deposited onto monovacancy graphene surface.

The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters

We present size dependent spin and orbital magnetic moments of cobalt (Con (+), 8 ≤ n ≤ 22), iron (Fen (+), 7 ≤ n ≤ 17), and nickel cluster (Nin (+), 7 ≤ n ≤ 17) cations as obtained by X-ray magnetic circular dichroism (XMCD) spectroscopy of isolated clusters in the gas phase. The spin and orbital magnetic moments range between the corresponding atomic and bulk values in all three cases. We compare our findings to previous XMCD data, Stern-Gerlach data, and computational results. We discuss the application of scaling laws to the size dependent evolution of the spin and orbital magnetic moments per atom in the clusters. We find a spin scaling law "per cluster diameter," ∼n(-1/3), that interpolates between known atomic and bulk values. In remarkable contrast, the orbital moments do likewise only if the atomic asymptote is exempt. A concept of "primary" and "secondary" (induced) orbital moments is invoked for interpretation.

Electronic structure of Zr-Ni-Sn systems: role of clustering and nanostructures in half-Heusler and Heusler limits

Half-Heusler and Heusler compounds have been of great interest for several decades for thermoelectric, magnetic, half-metallic and many other interesting properties. Among these systems, Zr-Ni-Sn compounds are interesting thermoelectrics which can go from semiconducting half-Heusler (HH) limit, ZrNiSn, to metallic Heusler (FH) limit, ZrNi2Sn. Recently Makongo et al (2011 J. Am. Chem. Soc. 133 18843) found that dramatic improvement in the thermoelectric power factor of HH can be achieved by putting excess Ni into the system. This was attributed to an energy filtering mechanism due to the presence of FH nanostructures in the HH matrix. Using density functional theory we have investigated clustering and nanostructure formation in ZrNi1+xSn (0 ⩽ x ⩽ 1) systems near the HH (x = 0) and FH (x = 1) ends and have found that excess Ni atoms in HH tend to stay close to each other and form nanoclusters. On the other hand, there is competing interaction between Ni-vacancies occupying different sites in FH which prevents them from forming vacancy nanoclusters. Effects of nano-inclusions on the electronic structure near HH and FH ends are discussed.

An optimized interatomic potential for Cu-Ni alloys with the embedded-atom method

We have developed a semi-empirical and many-body type model potential using a modified charge density profile for Cu-Ni alloys based on the embedded-atom method (EAM) formalism with an improved optimization technique. The potential is determined by fitting to experimental and first-principles data for Cu, Ni and Cu-Ni binary compounds, such as lattice constants, cohesive energies, bulk modulus, elastic constants, diatomic bond lengths and bond energies. The generated potentials were tested by computing a variety of properties of pure elements and the alloy of Cu, Ni: the melting points, alloy mixing enthalpy, lattice specific heat, equilibrium lattice structures, vacancy formation and interstitial formation energies, and various diffusion barriers on the (100) and (111) surfaces of Cu and Ni.

Density Functional Study of Structural and Electronic Properties of Small Bimetallic Silver−Nickel Clusters

Theoretical study on the structure and electronic properties of small AgmNip (m + p < or = 6) clusters has been carried out in the framework of density functional theory. Structural features, cohesive energies, vertical ionization potentials, and charge transfers are evaluated for each Ag/Ni ratio. In all the AgmNip clusters, the nickel atoms are brought together, yielding a maximum of Ni-Ni bonds, and the silver atoms are located around a Ni core with a maximum of Ag-Ni bonds. The ionization potential and the highest occupied molecular orbital shape are directly related to the two- or three-dimensional character of the cluster's geometry. A very low electronic charge transfer from Ni to Ag is found, and the magnetic moment is located on Ni atoms but with a low spin polarization on silver in the Ni-rich clusters.

Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters

Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (n<or=5), using the linear combination of Gaussian-type orbital density functional theory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.

Influence of Single Impurity Atoms on the Structure, Electronic, and Magnetic Properties of Ni5 Clusters

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.

Melting and Glass Transition for Ni Clusters

The melting of NiN clusters (N = 29, 50-150) has been investigated by using molecular dynamics (MD) simulations with a quantum corrected Sutton-Chen (Q-SC) many-body potential. Surface melting for Ni147, direct melting for Ni79, and the glass transition for Ni29 have been found, and those melting points are equal to 540, 680, and 940 K, respectively. It shows that the melting temperatures are not only size-dependent but also a symmetrical structure effect; in the neighborhood of the clusters, the cluster with higher symmetry has a higher melting point. From the reciprocal slopes of the caloric curves, the specific heats are obtained as 4.1 kB per atom for the liquid and 3.1 kB per atom for the solid; these values are not influenced by the cluster size apart in the transition region. The calculated results also show that latent heat of fusion is the dominant effect on the melting temperatures (Tm), and the relationship between S and L is given.

Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

The TaSi(n) (n=1-13) clusters with doublet, quartet, and sextet spin configurations have been systematically investigated by a relativistic density functional theory with the generalized gradient approximation available in Amsterdam density functional program. The total bonding energies, equilibrium geometries, Mulliken populations as well as Hirshfeld charges of TaSi(n) (n=1-13) clusters are calculated and presented. The emphasis on the stabilities and electronic properties is discussed. The most stable structures of the small TaSi(n) (n=1-6) clusters and the evolutional rule of low-lying geometries of the larger TaSi(n) (n=7-13) clusters are obtained. Theoretical results indicate that the most stable structure of TaSi(n) (n=1-6) clusters keeps the similar framework as the most stable structure of Si(n+1) clusters except for TaSi(3) cluster. The Ta atom in the lowest-energy TaSi(n) (n=1-13) isomers occupies a gradual sinking site, and the site moves from convex, to flatness, and to concave with the number of Si atom varying from 1 to 13. When n=12, the Ta atom in TaSi(12) cluster completely falls into the center of the Si frame, and a cagelike TaSi(12) geometry is formed. Meanwhile, the net Mulliken and Hirsheld populations of the Ta atom in the TaSi(n) (n=1-13) clusters vary from positive to negative, manifesting that the charges in TaSi(n) (n>/=12) clusters transfer from Si atoms to Ta atom. Additionally, the contribution of Si-Si and Si-Ta interactions to the stability of TaSi(n) clusters is briefly discussed. Furthermore, the investigations on atomic averaged binding energies and fragmentation energies show that the TaSi(n) (n=2,3,5,7,10,11,12) clusters have enhanced stabilities. Compared with pure silicon clusters, a universal narrowing of highest occupied molecular orbital-lowest unoccupied molecular orbital gap in TaSi(n) clusters is found.

Geometries and magnetisms of the Zrn (n=2–8) clusters: The density functional investigations

The geometries, stabilities, and electronic and magnetic properties of small-sized Zr(n) (n=2-8) clusters with different spin configurations were systematically investigated by using density functional approach. Emphasis is placed on studies that focus on the total energies, equilibrium geometries, growth-pattern behaviors, fragmentation energies, and magnetic characteristics of zirconium clusters. The optimized geometries show that the large-sized low-lying Zr(n) (n=5-8) clusters become three-dimensional structures. Particularly, the relative stabilities of Zr(n) clusters in terms of the calculated fragmentation energies and second-order difference of energies are discussed, exhibiting that the magic numbers of stabilities are n=2, 5, and 7 and that the pentagonal bipyramidal D(5h) Zr(7) geometry is the most stable isomer and a nonmagnetic ground state. Furthermore, the investigated magnetic moments confirm that the atomic averaged magnetic moments of the Zr(n) (n not equal to 2) display an odd-even oscillation features and the tetrahedron C(s) Zr(4) structure has the biggest atomic averaged magnetic moment of 1.5 mu(B)/at. In addition, the calculated highest occupied molecular orbital-lowest unoccupied molecular orbital gaps indicate that the Zr(n) (n=2 and 7) clusters have dramatically enhanced chemical stabilities.

Structure, stability, electronic and magnetic properties of Ni4 clusters containing impurity atoms

Using a gradient-corrected density functional method, we studied computationally how single impurity atoms affect the structure and the properties of a Ni4 cluster. H and O atoms coordinate at a Ni-Ni bond, inducing small changes to the structure of bare Ni4 which is essentially a tetrahedron. For a C impurity, we found three stable structures at a Ni4 cluster. In the most stable geometry, the carbon atom cleaves a Ni-Ni bond of Ni4, binding to all Ni atoms. Inclusion of the impurity atom leads to a partial oxidation of the metal atoms and, in the most stable structures, reduces the spin polarization of the cluster compared to bare Ni4. An H impurity interacts mainly with the Ni 4s orbitals, whereas the Ni 3d orbitals participate strongly in the bonding with O and C impurity atoms. For these impurity atoms, Ni 3d contributions dominate the character of the HOMO of the ligated cluster, in contrast to the HOMO of bare Ni4 where Ni 4s orbitals prevail. We also discuss a simple model which relates the effect of a H impurity on the magnetic state of metal clusters to the spin character (minority or majority) of the LUMO or HOMO of the bare metal cluster.

Continuation calculations of boron- (aluminum-, titanium-, and nickel-) doped La13 clusters

In this work, we have calculated boron-, aluminum-, titanium-, and nickel-doped La13 clusters by DMOL method based on the density-functional theory. Two doping modes are employed: surface and center doping. The boron, aluminum, and nickel atoms prefer to occupy the surface sites while the titanium atom prefers to occupy the center site. The doped La13 clusters with these four kinds of atoms have lower binding energy than pure La13 clusters. The icosahedral isomers are of lower binding energy than cubotahedral and decahedral isomers for La12B(-1), La12Al(-1), and La12Ni, while doping makes the cubotahedral La12Ti stable with a binding energy a little lower than icosahedral La12Ti. There are electronic shell effects in icosahedral La12B(-1) and La12Al(-1). The icosahedral La12B(-1) is promising to be formed during the doped process experimentally. Furthermore, we have also discussed the distorted structures of center doping by bond lengths, density of states, and charge transfers.

Homonuclear transition-metal trimers

Density-functional theory has been used to determine the ground-state geometries and electronic states for homonuclear transition-metal trimers constrained to equilateral triangle geometries. This represents the first application of consistent theoretical methods to all of the ten 3d block transition-metal trimers, from scandium to zinc. A search of the potential surfaces yields the following electronic ground states and bond lengths: Sc3(2A1',2.83 A), Ti3(7E',2.32 A), V3(2E",2.06 A), Cr3(17E',2.92 A), Mn3(16A2',2.73 A), Fe3(11E",2.24 A), Co3(6E",2.18 A), Ni3(3A2",2.23 A), Cu3(2E',2.37 A), and Zn3(1A1',2.93 A). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies DeltaE(M3-->M2+M) are 49.4 kcal mol(-1)(Sc3), 64.3 kcal mol(-1)(Ti3), 60.7 kcal mol(-1)(V3), 11.5 kcal mol(-1)(Cr3), 32.4 kcal mol(-1)(Mn3), 61.5 kcal mol(-1)(Fe3), 78.0 kcal mol(-1)(Co3), 86.1 kcal mol(-1)(Ni3), 26.8 kcal mol(-1)(Cu3), and 4.5 kcal mol(-1)(Zn3).